Inquiring Minds

I have a question, but first, thank you for the terrific new web site. You
did a fantastic job.

Question:

Where does present theory say the energy of a red shifted photon goes?

The idea that universal expansion is responsible for the red shift of
intergalactic light would seem correct if light were a continuous wave.
However, since a photon is a quantum of energy, and since the entire photon
is presumably captured, the photon should still have the same amount of
energy when the packet is fully captured even if it was stretched by
universal expansion, unless of course the photon is loosing energy in
transit, which it must do to not conflict with Planck's equation. And if a
photon looses energy in transit, there is no need to claim universal
expansion.

There is a fundamental conflict here and I would very much like to know how
it is presently resolved. The only logical answer I see is the photon must
loose energy traveling great distances in space. (I realize they don't think
a photon can loose energy to a vacuum, but they also don't think a vacuum is
empty.)

This is not as general of question as you might like, but I cannot find the
answer anywhere.

Thank you for considering answering my question,
David Rees

Dear Mr. Rees,

Your question about the redshift of a single photon is a great one. It really
gets to the heart of the meaning of redshift and the expansion of the
universe. The solution to the dilemma, however, lies in a careful
consideration of the viewpoint of the observer who is measuring the energy of
the photon.

As you know, the basic idea of redshift is that when a source of light
recedes from us, the crests and troughs of the wave (actually the peaks in
the electric and magnetic fields that make up light) get delayed by the
motion of the source. We see a longer wavelength than was emitted by the
source. In the case of light in the visible portion of the electromagnetic
spectrum, we see light shifted to the longer-wavelength or redder portion of
the spectrum. Thus, the spectrum of stars and galaxies is "redshifted" when
the source of light is moving away from us. Faraway sources are moving away
from us because of the expansion of the universe. Your question is about what
this means for the energy carried by the light, because the energy and the
frequency of light are related. E=h*f, where f is the frequency of the light.

First, let's put aside the idea of the photon losing energy in transit, as an
explanation for redshift. A photon doesn't lose energy unless it collides
with a particle. Photons can scatter off interstellar electrons, for example.
(Perhaps you were thinking about particles, like electrons, losing energy "in
transit" in a vacuum. That can happen if they change direction. Electrons
radiate and lose energy if they travel on a curved path around a magnetic
field line.) Photons carry energy, but they don't lose energy just because
they travel.

The key to understanding the dilemma of a red-shifted photon is that not all
observers will measure the same energy of the photon. Let's say an observer
is traveling with the star or galaxy and sees a photon in the yellow portion
of the spectrum. An observer who is moving with respect to the star (it
doesn't matter if it's the star or the observer moving away) sees the same
photon in the red part of the spectrum. That's OK--it doesn't violate the
principle of conservation of energy--because they make their measurements in
different reference frames. Similarly if you roll a marble while you are
riding on a train, you will find that the marble has a certain velocity and
kinetic energy as seen from your seat in the train, but an observer in the
train station, who (somehow) sees the marble as it goes whipping by on the
train, measures a different velocity and hence a different kinetic energy.
The energy of a photon comes from its frequency, and that is different for
different observers.

[It can be confusing to think about the conservation of energy and
measurements made from different reference frames. Keep in mind that energy
is conserved within each reference frame, or (to put it another way) for two
observers who are moving at the same speed with respect to the thing they
observe. Consider an observer on earth and an observer who is close to the
galaxy of interest, but moving away from the galaxy at the same speed that
the observer on earth is moving away from the galaxy. These two observers are
in the same reference frame, even if they are separated by millions of miles.
They measure the same energy carried by a photon from the galaxy. But the
value they come up with for the energy is different from that obtained by an
observer in the same frame as the galaxy, or any other reference frame.]

The argument I've given you does not depend on special relativity, but you
can find a good discussion of the importance of the observer's reference
frame in the book "Space and Time in Special Relativity" by N. David Mermin
of Cornell University. I think you would enjoy it.